Diffusiophoresis under gradients of a neutral solute. For any radially symmetric potential \({\cal U}(r)\) , one may compute an exact solution of (REF ) for the velocity profile by extending textbook techniques for the Stokes problem in [1]} (see also [2]} for a related calculation in the context of electrophoresis). It can be demonstrated that the solution for \(\mathbf {v}(\mathbf {r})\)  involves a Stokeslet as a leading term, which allows to calculate the force along the axis of the gradient as the prefactor of the Stokeslet term (\(v\sim F/r\) ). This allows to deduce the global force on the particle as
\(F= 6 \pi R \eta v_{DP}- 2 \pi R^2 \int _R^{\infty } c_0(r) (-\partial _r{\cal U})(r) \times \varphi (r) dr\) 
